Question

Math Help Please,I'm stuck!

How many Solutions does this System Have?

{-5x-y=5
x-2y=-1

1. Infinitely many solutions
2. No solutions
3. Two solutions
4. One Solution

2. Solve the System {8y=4x-16
-x=-2y-4

1. (12,3)
2. No solution
3. (8, -4)
4. Infinite Solutions

3. Which point is part of the solution of the inquality y≤|x+2|-3

1. (0,1)
2. (-1,-1)
3. (1,0)
4. (0,0)

Any help would be extremely appreciated!

Answer 1

1. -5x - y = 5.......y = -5x - 5....slope = -5 and y int = -5
x - 2y = -1......y = 1/2x + 1/2...slope = 1/2 and y int = 1/2
different slopes, different y int = 1 solution
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2. 8y = 4x - 16
y = 1/2x - 2....slope = 1/2, y int = -2

-x = -2y - 4
2y = x - 4
y = 1/2x - 2...slope = 1/2, y int = -2

same slope, same y int = infinite solutions
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3. y <= | x + 2| - 3 ...subbing in (1,0)

0 < = | 1 + 2| - 3
0 < = 3 - 3
0 < = 0 (correct)....so ur answer is (1,0)